Solve for $x$ and $y$ using substitution. ${5x+6y = 4}$ ${y = -4x+7}$
Since $y$ has already been solved for, substitute $-4x+7$ for $y$ in the first equation. ${5x + 6}{(-4x+7)}{= 4}$ Simplify and solve for $x$ $5x-24x + 42 = 4$ $-19x+42 = 4$ $-19x+42{-42} = 4{-42}$ $-19x = -38$ $\dfrac{-19x}{{-19}} = \dfrac{-38}{{-19}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -4x+7}\thinspace$ to find $y$ ${y = -4}{(2)}{ + 7}$ $y = -8 + 7$ $y = -1$ You can also plug ${x = 2}$ into $\thinspace {5x+6y = 4}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 6y = 4}$ ${y = -1}$